Plane on a coneyor belt
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@ Remus. No. Acceleration to infinity is impossible. That means that the entire model is invalid, it does not mean that the plane can't take off. You could just as easily argue that the travelator can't accelerate to infinity, therefore the plane CAN take off.
The wheels could only spin infinitely fast if the conveyor was also travelling infinitely fast. In practice the wheels wouldn't spin infinitely fast...they'd go as fast as they could, then they'd skid, adding a slight extra friction, but nothing that amounted to anything serious.@ plot-paris. No. For the umteenth time, the speed of the conveyor is irrelevent. The conveyor can only exert a small amount of reverse force in the form of friction on the plane. This is equivalent to (depending on the size of the plane) between 1 manpower and a couple of horsepower. It is also constant whatever the speed of the conveyor. Admittedly, more work will be done as the conveyor accelerates and the wheels spin faster. However, all that extra energy will be supplied by the conveyor, not deducted from the plane's thrust. It is the conveyor that is making the wheels spin faster than they would ordinarily need to. That work energy is rotational, not directional; it has no effect on the forward motion of the plane.
The plane, on the other hand has its full forward thrust available. It will move forward through the air nearly as normal. Where are you getting this no wind pressure from?
Are you really saying that a man with a rope tied around the tail of a plane can stop it taking off by pulling backwards? Chuck Norris could, of course.
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of course we all know, that chuck norris would never do that, because he enjoys us mortals struggling with this problem
ok. we all agree with the fact, that the plane has to move forward to take off, right (because it needs to move foreward to get air pressure under it's wings). of course we all know as well, that to achieve this foreward movement, the plane doesn't need this upward lift (that is merely a result of the forward movement).
so our whole difference lies in the question, if the conveyor, moving backwards, can transfer any energy in form of motion through the wheels to the plane.
you say that the wheels do not have the option to transfer this energy to the plane whatsoever.
and I completely disagree with that. let me tell you again, why:if you place pav's skate board on the treadmill again and switch it on, it will be transported backwards and fall off.
to prevent this, you hold your finger against the board - it stays stationary
if you remove your finger, the board will move backwards and fall off!that demonstrates, that energy was necessary to keep the board in place.
the kinetic energy was transferred from the treadmill, through the wheels, to the board due to the frictional resistance - thereby was transformed to heat-energy in the wheels.
if you speed up the treadmill, the tyres will heat up quicker, than with low speed. at the same time you need slightly more energy to keep the board in place on the treadmill.
and that demonstrates, that increasing the speed of the conveyor increases the kinetic energy transferred to the plane - therefore the theoretical possiblility to prevent the forward-movement of the plane is proven!
ps: nice argumentation with infinity, remus. would never have thought to take it thus far
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Ok, i think ive come up with a neat mathematical way of explaing this.
First, the question states that the conveyor belt will always match the speed of the wheel, so if we call wheel speed 'x' and conveyor speed 'y':
x=y
For the plane to take off it must have forward velocity of say 100 mph, this can be expressed as:
y+100
if we take to be any speed the conveyor had before the forward velocity.
so at the moment of take off:
x=y+100
Looking back at our first equation
x=y
and
x=y+100
cannot both be true at the same time.
EDIT: i realised a flaw in the original argument, and changed it.
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I am afraid, this is not correct, for you assume that the entire speed of the conveyor (Y) will be transferred to the plane, which is not correct.
we had to introduce the variable of the frictional resistance (f). so the objective speed of the plane (OS) would be (the speed the plane normally would travel is hence called SuS (for Subjective Speed)):
OS = SuS - Y*f
[Edit]
and to calculate Y:
Y = SuS*f
[Edit2]
Sorry, wrong again:
OS = SuS - Y/f
Y = SuS*f
therefore: OS = Sus - Sus*f/f
therefore: OS = Sus - Sus
therefore: OS = 0
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The basic premise behind the argument stays the same, though.
EDIT: (i think
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pav, we two have to agree with one of the answers for this question and then produce a SCF-TV episode.
because we all know: what you see on television news is bound to be true
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exactly!
TV never lies, it's the people in front of the cameras that do.
he he
pav
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There is some really bad maths and physics going on here. Mix that with architecture and it gets a little scary. Make sure you have good engineers guys.
Sorry, but I have now lost the will to live.
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Alan, if you can explain to me in a sensible way, why the skateboard should NOT fall off the treadmill (my example from 8 posts above), when no finger is holding it on it's position, you will have convinced mee...
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yes it is indeed. only that it is work (and my boss) calling at the moment
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If nothing else thats a pretty funny cartoon.
If you ever recover the will to live, i'm interested to know where the flaw is in my argument
You lost me with your thing about friction jakob...
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Remus, The terms aren't defined nearly precisely enough.
I think we can probably agree that conveyor speed would be that speed as observed by somone at a fixed point at the side of the conveyor. I think we can also agree that the plane's speed would be its forward motion through the air (assuming no wind and again relative to a fixed observer).But what the heck is "wheel speed"? Do you mean the speed at the bottom of the wheel...where it makes contact with the conveyor? Is that relative to a fixed observer or relative to the conveyor it is rolling over? Do you mean the speed of the hub (which would be the same as the plane's speed)? Or do you mean the speed of the wheel at the TDC (which would not be simply a negative value of the speed at the bottom, because you would need to add any forward motion of the plane to that).
Unless you are clear about your frames of reference you can make some very basic errors...like the equation. The way it is phrased creates a circular argument that allows the plane no forward motion. All it says is the plane remains static because it's static, therefore it can't take off. No kidding? That's why you end up with two irreconcilable functions...because you artificially injected a plane speed (+100) into an argument that prohibited a plane speed.
Jakob, of course the skateboard will fall off if it has no forward power. I thought we were discussing a plane that was powering forward? The skateboard however will not move backwards at the same speed as the treadmill.
If you don't believe me, I repeat, place a sheet of A4 on the table. Place a roll of tape on top of it and pull the sheet back at something like treadmill speed.The treadmill will transport the skateboard backwards...but only by as much as friction will allow, it's not like transporting it tied down on the back of a truck.
As I said before, this friction will remain constant regardless of the speed of the treadmill. Pulling that paper faster is not going to make the roll of tape go backwards faster...in fact it might even stand still or move forwards.All the business regarding the speed of the wheels is irrelevant...it has no direction, therefore can't counter any movement. All that is happening is that the wheels are storing potential energy so that they would rocket the skateboard forwards if the treadmill were to suddenly stop. There is no equation you can quote that will demonstrate that you need more force to keep the skateboard static as the treadmill increases its speed. The only point of contact between the two is the bottom of the wheels and the only force at play is friction. Friction is a function of the coefficient of friction and weight. Speed has nothing to do with it. Yes the wheels will get hotter with increased speed. That's simply because the amount of kinetic energy being transferred is outstripping the ability of the atmosphere to dispel the resulting heat. It has no more effect on the motion of the skateboard than if you were to siphon off that energy some other way, pass it through a dynamo and point an electric fire at the skateboard.
Increasing the speed of the treadmill has the same effect as increasing the speed of the paper under the tape...none at all.You made an analogy earlier to someone on a bike hanging off the back of a moving vehicle and stated that the force on their arm would increase the faster that vehicle went. No it wouldn't. It would only increase by two means a) if they were subjected to increased air resistance, or b) while the vehicle was actually accelerating. Once it reached a higher speed the pull on the cyclist's arm would be exactly the same as before.
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...or putting it very much simpler:-
Remus, you already agreed that the plane would be able to take off in your first example. It could take off because the speed of the conveyor is irrelevant.Would you mind explaining to me what is different in the second example? Irelevant means irrelevant....whether the conveyor is travelling at a constant speed or accelerating in direct ratio to the wheel speed or anything else in the Universe.
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I just thought about the wheel of my brother's racing cycle. if I spin it as fast as I can, it will take a minute to come to a halt (due to the small amount of frictional resistance).
so I agree with you, that practically, it is impossible to use this tiny amount of force applyable to stop the plane from moving forward.
but I allways had the impression, that the bycicle wheel lost most of it's speed at the beginning. I believe, that the slow down does not happen in a linear way, but in a curve. that would mean, that speed does matter!
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To try and define what i meant by wheel speed, i suppose youd call it the rotational speed of the wheel multiplied by the circumfrence of the wheel.
In the first question what happens to the wheels is entirely possible. In the second question what is happening to the wheels is entirely impossible.
EDIT:I started to write out a big long reply, but i hit a mental blank. Give me a while to ponder. You may have won me over alan
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Jakob, i find it hard to believe you can accurately judge the speed of a wheel just by looking at it...
And speed does play a part in air resistance, but not in frictional resistance.
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well that was just my objective observation.
but for friction (or lets call it Rolling resistance) speed does play a part!
http://en.wikipedia.org/wiki/Rolling_resistance#cite_note-Hibbeler-0@unknownuser said:
Additional factors include wheel radius, and forward speed
I tried to do some calculations. I used the Eurofighter 2000 Typhoon as an example (because it is the best fighter jet Europe can provide
).according to the formula provided by wikipedia, the rolling resistance of the Eurofighter 2000 is:
(I asumed the jet's tires to be equivalent to a Low-resistance car tire on a smooth road)1,53 kN
the thrust of the jet engines (without afterburner) is:
60 kN
unfortunately I did not find a formula that contained a speed-variable...
Can someone check this? the rolling resistance seems a bit too high to me (in relation to the thrust of the engines...) -
@remus said:
To try and define what i meant by wheel speed, i suppose youd call it the rotational speed of the wheel multiplied by the circumfrence of the wheel.
That's where you are going wrong. All other observations have been made from the point of view of a static observer at the side of the conveyor belt.
If you only allow for a single "wheel speed" you will only achieve that by keeping the wheel absolutely stationary relative to such an observer and having it spin on the spot. You have, in effect tethered the plane before it even gets going. Either that or you have suddenly switched from being a static observer to one travelling alongside the plane, completely altering the frame of reference.In reality, to a static observer the wheel speed at the top of the wheel would be the sum of your rotational speed plus any forward motion of the aircraft.
At the bottom of the wheel it would be the rotational speed (obviously minus, if we are using vectors) minus the speed of the aircraft.The plane can only move in either direction if the two opposing speeds differ from one another, relative to a static point. If they are held to be the same, then they cancel each other out and the wheel (and plane) ain't going nowhere.
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Alan's right. There's no complicated physics required (especially crock physics) to resolve it. The wheels on the plane are irrelevant- they have negligible effect on the forward motion of the plane. In fact that's the whole point of the wheels, unlike driven car wheels, plane wheels are there to isolate the plane from it's surroundings- i.e. to reduce the friction between the plane and the ground to the point that it is negligible.... until the brakes are applied.
The wheels are irrelevant, the conveyor belt is irrelevant, the lift of the plane is irrelevant, the crux of the problem is simply: do jet planes propel themselves forward when their jet engines are fired up? Of course they do, whether they're on land, in the air or in a vacuum (well rocket engines in the last case).
Now if the plane was in a wind tunnel which could match the velocity of the plane's jet engines, that would be a different problem altogether (but just as easily solved).
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